摘要:
本文研究了特征为3的椭圆曲线密码体制中标量乘的快速算法，并针对底层运算和上层运算分别进行改进。在底层运算中，采用递推归纳、乘法代替求逆、立方代替乘法的思想提出在仿射坐标下直接计算3kP的算法，将求逆运算降至1次；在上层运算中，采用滑动窗口标量乘的方法，既有效减少了非零窗口的长度又减少了算法中3倍点总的运算量。
In this paper we investigate the fast algorithm of scalar multiplication based on Elliptic Curve Cryptography (ECC) over fields of characteristic three, and make improvements both in underlying operations and upper operations respectively. In the underlying operations, we deduce a formula of calculating 3kP directly under the affine coordinates based upon the idea of recursion, trading inversion for multiplication and trading multiplication for cube, which reduces the inversion to once; in the upper operations, we adopt the sliding window scalar multiplication method, which reduces the length of the non-zero windows and the total computations of 3P effectively.